Various types of measuring devices are used for the high-precision optical determination of distance or position. First of all, interferometers without physically formed measuring standards are used for determining distance; secondly, interferential position-measuring devices having physically formed measuring standards are used for determining position.
In the case of measuring devices in the form of interferometers, problems are discussed in the following that occur particularly in connection with familiar plane-mirror interferometers. Such plane-mirror interferometers are described, for example, in U.S. Pat. No. 4,693,605 and U.S. Pat. No. 5,064,289. FIG. 1a schematically illustrates a conventional a plane-mirror interferometer.
Beam of rays S emitted by a light source—not shown in FIG. 1a—is split, for example, via a splitting element ST in the form of a polarization-optical beam splitter into two sub-beams. The two sub-beams are a measuring beam M and a reference beam R. Measuring beam M is then reflected by an optical functional element, which in the present case is in the form of a measuring reflector or plane mirror P, and directed via splitting element ST to a measuring retroreflector MR. For example, the retroreflector may take the form of a triple prism or triple mirror. Measuring retroreflector MR deflects measuring beam M exactly the opposite direction, back to plane mirror P again. There, measuring beam M is reflected again before it propagates back in the direction of splitting element ST, where it comes to interfering superposition with reference beam R which was deflected beforehand via a reference retroreflector RR. Downstream of splitting element ST on the output side is a detector system—also not shown in FIG. 1a. A phase-encoded measuring signal is able to be generated from the superposed sub-beams via the detector system, the measuring signal representing a measure for the distance of plane mirror P from the remaining components of the interferometer.
Even if, according to FIG. 1b, plane mirror P is tilted slightly by an angle α relative to its setpoint position, after the second reflection at plane mirror P, measuring beam M extends exactly anti-parallel to originally incident beam of rays S prior to the first reflection at plane mirror P. In this manner, measuring beam M may subsequently be superposed with reference beam R in beam splitter ST, without an angle shear or directional shear occurring. However, measuring beam M is shifted laterally by a small tilting of plane mirror P, so that after being recombined, the measuring beam and the reference beam are no longer superposed over the entire beam cross-section, i.e., a location shear results with regard to the beams of rays involved in the signal generation. Therefore, the interference occurs only in the reduced overlapping region, as a consequence of which, the resulting amplitude or the degree of modulation of the phase-encoded measuring signals generated in this manner is reduced.
Therefore, a minimum cross-section of beam of rays S must be provided for a predefined tilt tolerance of plane mirror P, in order to limit the signal drop caused in such a manner. This relationship is described for a Gaussian beam of rays S, which is emitted by a light source in the form of a laser, by the following equations (1a) and (1b), respectively:
                              η          =                      ⅇ                                          -                8                            ·                                                (                                                                                    L                        Max                                            ·                                              α                        Max                                                              w                                    )                                2                                                    ⁢                                  ⁢        and                            (                  equation          ⁢                                          ⁢          1          ⁢          a                )                                w        =                              2            ⁢                                          2                            ·                              L                Max                            ·                              α                Max                                                                        ln              ⁡                              (                                  η                                      -                    1                                                  )                                                                        (                  equation          ⁢                                          ⁢          1          ⁢          b                )            in which LMax represents the maximum distance of the plane mirror from the measuring retroreflector, αMax represents the maximum tilt angle of the plane mirror, w represents 1/e2-beam cross-section of the beam of rays, η represents the minimum permissible signal level relative to the signal level, when the plane mirror is not tilted.
With LMax=2m, αMax=1 mrad and η=0.7 (signal drop to 70%), a minimum beam cross-section w of beam of rays S according to w=9.5 mm is obtained. Since the wavefront of beam of rays S must be very even over the beam cross-section (typical requirement: λ/10), correspondingly complicated and costly collimating optics are needed to collimate beam of rays S, without a considerable signal drop being absolutely unavoidable. Such a signal drop leads to a decrease in accuracy in the determination of distance by the interferometer, and to an increased signal noise in the measuring signals generated. Furthermore, the small tilt tolerance of plane mirror P is naturally also annoying if one takes into account that it includes both the assembly tolerance and the operating tolerance.
Similar problems also result in the case of the interferential position-measuring devices mentioned above, having physically formed measuring standards. The tilting of optical functional elements in the scanning beam path out of their setpoint position affect the generated measuring signals negatively, as well. The corresponding position-measuring devices usually include a measuring standard as an optical functional element. Relatively movable to this along at least one measuring direction, a scanning unit is provided having various further optical components such as a light source, a splitting element, a retroreflector, and a detector system. Such position-measuring devices react particularly sensitively to tilts of the scanning unit and/or measuring standard about a normal to the measuring standard. Such a tilt is also referred to as moiré tilting. Because of the retroreflectors frequently provided in these devices on the part of the scanning unit, an angle shear or directional shear of the interfering sub-beams is able to be minimized, however, a location shear of the split sub-beams remains, which limits the maximum permissible moiré tilt angle. Consequently, the maximum permissible moiré tilt angle is usually markedly less for this type of measuring devices than the maximum permissible tilt angles about the two remaining tilt axes, e.g., about the “longitudinal axis” and the “horizontal axis.”